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Adaptive nonparametric estimation of a component density in a two-class mixture model

Chagny, Gaëlle; Channarond, Antoine; Hoang, Van Ha; Roche, Angelina (2022), Adaptive nonparametric estimation of a component density in a two-class mixture model, Journal of Statistical Planning and Inference, 216, p. 51-69. 10.1016/j.jspi.2021.05.004

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Type
Article accepté pour publication ou publié
Date
2022
Journal name
Journal of Statistical Planning and Inference
Volume
216
Publisher
Elsevier
Pages
51-69
Publication identifier
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Author(s)
Chagny, Gaëlle
Laboratoire de Mathématiques Raphaël Salem [LMRS]
Channarond, Antoine
Laboratoire de Mathématiques Raphaël Salem [LMRS]
Hoang, Van Ha
Laboratoire de Mathématiques Raphaël Salem [LMRS]
Roche, Angelina
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
A two-class mixture model, where the density of one of the components is known, is considered. We address the issue of the nonparametric adaptive estimation of the unknown probability density of the second component. We propose a randomly weighted kernel estimator with a fully data-driven bandwidth selection method, in the spirit of the Goldenshluger and Lepski method. An oracle-type inequality for the pointwise quadratic risk is derived as well as convergence rates over Hölder smoothness classes. The theoretical results are illustrated by numerical simulations.
Subjects / Keywords
two-class mixture model; Goldenshluger and Lepski method